Data encryption standard (DES) | Set 1

• Difficulty Level : Hard
• Last Updated : 08 Nov, 2021

Data encryption standard (DES) has been found vulnerable against very powerful attacks and therefore, the popularity of DES has been found slightly on the decline.
DES is a block cipher and encrypts data in blocks of size of 64 bits each, which means 64 bits of plain text goes as the input to DES, which produces 64 bits of ciphertext. The same algorithm and key are used for encryption and decryption, with minor differences. The key length is 56 bits. The basic idea is shown in the figure.

We have mentioned that DES uses a 56-bit key. Actually, the initial key consists of 64 bits. However, before the DES process even starts, every 8th bit of the key is discarded to produce a 56-bit key. That is bit positions 8, 16, 24, 32, 40, 48, 56, and 64 are discarded. 

Thus, the discarding of every 8th bit of the key produces a 56-bit key from the original 64-bit key.
DES is based on the two fundamental attributes of cryptography: substitution (also called confusion) and transposition (also called diffusion). DES consists of 16 steps, each of which is called a round. Each round performs the steps of substitution and transposition. Let us now discuss the broad-level steps in DES. 

1. In the first step, the 64-bit plain text block is handed over to an initial Permutation (IP) function.
2. The initial permutation is performed on plain text.
3. Next, the initial permutation (IP) produces two halves of the permuted block; says Left Plain Text (LPT) and Right Plain Text (RPT).
4. Now each LPT and RPT go through 16 rounds of the encryption process.
5. In the end, LPT and RPT are rejoined and a Final Permutation (FP) is performed on the combined block
6. The result of this process produces 64-bit ciphertext.

Initial Permutation (IP) – 
As we have noted, the initial permutation (IP) happens only once and it happens before the first round. It suggests how the transposition in IP should proceed, as shown in the figure. 
For example, it says that the IP replaces the first bit of the original plain text block with the 58th bit of the original plain text, the second bit with the 50th bit of the original plain text block, and so on.
This is nothing but jugglery of bit positions of the original plain text block. the same rule applies to all the other bit positions shown in the figure.

As we have noted after IP is done, the resulting 64-bit permuted text block is divided into two half blocks. Each half-block consists of 32 bits, and each of the 16 rounds, in turn, consists of the broad level steps outlined in the figure. 

Step-1: Key transformation – 
We have noted initial 64-bit key is transformed into a 56-bit key by discarding every 8th bit of the initial key. Thus, for each a 56-bit key is available. From this 56-bit key, a different 48-bit Sub Key is generated during each round using a process called key transformation. For this, the 56-bit key is divided into two halves, each of 28 bits. These halves are circularly shifted left by one or two positions, depending on the round.
For example, if the round numbers 1, 2, 9, or 16 the shift is done by only position for other rounds, the circular shift is done by two positions. The number of key bits shifted per round is shown in the figure.

After an appropriate shift, 48 of the 56 bits are selected. for selecting 48 of the 56 bits the table is shown in the figure given below. For instance, after the shift, bit number 14 moves on the first position, bit number 17 moves on the second position, and so on. If we observe the table carefully, we will realize that it contains only 48-bit positions. Bit number 18 is discarded (we will not find it in the table), like 7 others, to reduce a 56-bit key to a 48-bit key. Since the key transformation process involves permutation as well as a selection of a 48-bit subset of the original 56-bit key it is called Compression Permutation.

Because of this compression permutation technique, a different subset of key bits is used in each round. That makes DES not easy to crack.

Step-2: Expansion Permutation – 
Recall that after initial permutation, we had two 32-bit plain text areas called Left Plain Text(LPT) and Right Plain Text(RPT). During the expansion permutation, the RPT is expanded from 32 bits to 48 bits. Bits are permuted as well hence called expansion permutation. This happens as the 32-bit RPT is divided into 8 blocks, with each block consisting of 4 bits. Then, each 4-bit block of the previous step is then expanded to a corresponding 6-bit block, i.e., per 4-bit block, 2 more bits are added. 

This process results in expansion as well as a permutation of the input bit while creating output. The key transformation process compresses the 56-bit key to 48 bits. Then the expansion permutation process expands the 32-bit RPT to 48-bits. Now the 48-bit key is XOR with 48-bit RPT and the resulting output is given to the next step, which is the S-Box substitution.

• C++
• Java
• Python

#include <bits/stdc++.h>

using namespace std;

string hex2bin(string s)

{

    // hexadecimal to binary conversion

    unordered_map<char, string> mp;

    mp['0'] = "0000";

    mp['1'] = "0001";

    mp['2'] = "0010";

    mp['3'] = "0011";

    mp['4'] = "0100";

    mp['5'] = "0101";

    mp['6'] = "0110";

    mp['7'] = "0111";

    mp['8'] = "1000";

    mp['9'] = "1001";

    mp['A'] = "1010";

    mp['B'] = "1011";

    mp['C'] = "1100";

    mp['D'] = "1101";

    mp['E'] = "1110";

    mp['F'] = "1111";

    string bin = "";

    for (int i = 0; i < s.size(); i++) {

        bin += mp[s[i]];

    }

    return bin;

}

string bin2hex(string s)

{

    // binary to hexadecimal conversion

    unordered_map<string, string> mp;

    mp["0000"] = "0";

    mp["0001"] = "1";

    mp["0010"] = "2";

    mp["0011"] = "3";

    mp["0100"] = "4";

    mp["0101"] = "5";

    mp["0110"] = "6";

    mp["0111"] = "7";

    mp["1000"] = "8";

    mp["1001"] = "9";

    mp["1010"] = "A";

    mp["1011"] = "B";

    mp["1100"] = "C";

    mp["1101"] = "D";

    mp["1110"] = "E";

    mp["1111"] = "F";

    string hex = "";

    for (int i = 0; i < s.length(); i += 4) {

        string ch = "";

        ch += s[i];

        ch += s[i + 1];

        ch += s[i + 2];

        ch += s[i + 3];

        hex += mp[ch];

    }

    return hex;

}

string permute(string k, int* arr, int n)

{

    string per = "";

    for (int i = 0; i < n; i++) {

        per += k[arr[i] - 1];

    }

    return per;

}

string shift_left(string k, int shifts)

{

    string s = "";

    for (int i = 0; i < shifts; i++) {

        for (int j = 1; j < 28; j++) {

            s += k[j];

        }

        s += k[0];

        k = s;

        s = "";

    }

    return k;

}

string xor_(string a, string b)

{

    string ans = "";

    for (int i = 0; i < a.size(); i++) {

        if (a[i] == b[i]) {

            ans += "0";

        }

        else {

            ans += "1";

        }

    }

    return ans;

}

string encrypt(string pt, vector<string> rkb, vector<string> rk)

{

    // Hexadecimal to binary

    pt = hex2bin(pt);

    // Initial Permutation Table

    int initial_perm[64] = { 58, 50, 42, 34, 26, 18, 10, 2,

                             60, 52, 44, 36, 28, 20, 12, 4,

                             62, 54, 46, 38, 30, 22, 14, 6,

                             64, 56, 48, 40, 32, 24, 16, 8,

                             57, 49, 41, 33, 25, 17, 9, 1,

                             59, 51, 43, 35, 27, 19, 11, 3,

                             61, 53, 45, 37, 29, 21, 13, 5,

                             63, 55, 47, 39, 31, 23, 15, 7 };

    // Initial Permutation

    pt = permute(pt, initial_perm, 64);

    cout << "After initial permutation: " << bin2hex(pt) << endl;

    // Splitting

    string left = pt.substr(0, 32);

    string right = pt.substr(32, 32);

    cout << "After splitting: L0=" << bin2hex(left)

         << " R0=" << bin2hex(right) << endl;

    // Expansion D-box Table

    int exp_d[48] = { 32, 1, 2, 3, 4, 5, 4, 5,

                      6, 7, 8, 9, 8, 9, 10, 11,

                      12, 13, 12, 13, 14, 15, 16, 17,

                      16, 17, 18, 19, 20, 21, 20, 21,

                      22, 23, 24, 25, 24, 25, 26, 27,

                      28, 29, 28, 29, 30, 31, 32, 1 };

    // S-box Table

    int s[8][4][16] = { { 14, 4, 13, 1, 2, 15, 11, 8, 3, 10, 6, 12, 5, 9, 0, 7,

                          0, 15, 7, 4, 14, 2, 13, 1, 10, 6, 12, 11, 9, 5, 3, 8,

                          4, 1, 14, 8, 13, 6, 2, 11, 15, 12, 9, 7, 3, 10, 5, 0,

                          15, 12, 8, 2, 4, 9, 1, 7, 5, 11, 3, 14, 10, 0, 6, 13 },

                        { 15, 1, 8, 14, 6, 11, 3, 4, 9, 7, 2, 13, 12, 0, 5, 10,

                          3, 13, 4, 7, 15, 2, 8, 14, 12, 0, 1, 10, 6, 9, 11, 5,

                          0, 14, 7, 11, 10, 4, 13, 1, 5, 8, 12, 6, 9, 3, 2, 15,

                          13, 8, 10, 1, 3, 15, 4, 2, 11, 6, 7, 12, 0, 5, 14, 9 },

                        { 10, 0, 9, 14, 6, 3, 15, 5, 1, 13, 12, 7, 11, 4, 2, 8,

                          13, 7, 0, 9, 3, 4, 6, 10, 2, 8, 5, 14, 12, 11, 15, 1,

                          13, 6, 4, 9, 8, 15, 3, 0, 11, 1, 2, 12, 5, 10, 14, 7,

                          1, 10, 13, 0, 6, 9, 8, 7, 4, 15, 14, 3, 11, 5, 2, 12 },

                        { 7, 13, 14, 3, 0, 6, 9, 10, 1, 2, 8, 5, 11, 12, 4, 15,

                          13, 8, 11, 5, 6, 15, 0, 3, 4, 7, 2, 12, 1, 10, 14, 9,

                          10, 6, 9, 0, 12, 11, 7, 13, 15, 1, 3, 14, 5, 2, 8, 4,

                          3, 15, 0, 6, 10, 1, 13, 8, 9, 4, 5, 11, 12, 7, 2, 14 },

                        { 2, 12, 4, 1, 7, 10, 11, 6, 8, 5, 3, 15, 13, 0, 14, 9,

                          14, 11, 2, 12, 4, 7, 13, 1, 5, 0, 15, 10, 3, 9, 8, 6,

                          4, 2, 1, 11, 10, 13, 7, 8, 15, 9, 12, 5, 6, 3, 0, 14,

                          11, 8, 12, 7, 1, 14, 2, 13, 6, 15, 0, 9, 10, 4, 5, 3 },

                        { 12, 1, 10, 15, 9, 2, 6, 8, 0, 13, 3, 4, 14, 7, 5, 11,

                          10, 15, 4, 2, 7, 12, 9, 5, 6, 1, 13, 14, 0, 11, 3, 8,

                          9, 14, 15, 5, 2, 8, 12, 3, 7, 0, 4, 10, 1, 13, 11, 6,

                          4, 3, 2, 12, 9, 5, 15, 10, 11, 14, 1, 7, 6, 0, 8, 13 },

                        { 4, 11, 2, 14, 15, 0, 8, 13, 3, 12, 9, 7, 5, 10, 6, 1,

                          13, 0, 11, 7, 4, 9, 1, 10, 14, 3, 5, 12, 2, 15, 8, 6,

                          1, 4, 11, 13, 12, 3, 7, 14, 10, 15, 6, 8, 0, 5, 9, 2,

                          6, 11, 13, 8, 1, 4, 10, 7, 9, 5, 0, 15, 14, 2, 3, 12 },

                        { 13, 2, 8, 4, 6, 15, 11, 1, 10, 9, 3, 14, 5, 0, 12, 7,

                          1, 15, 13, 8, 10, 3, 7, 4, 12, 5, 6, 11, 0, 14, 9, 2,

                          7, 11, 4, 1, 9, 12, 14, 2, 0, 6, 10, 13, 15, 3, 5, 8,

                          2, 1, 14, 7, 4, 10, 8, 13, 15, 12, 9, 0, 3, 5, 6, 11 } };

    // Straight Permutation Table

    int per[32] = { 16, 7, 20, 21,

                    29, 12, 28, 17,

                    1, 15, 23, 26,

                    5, 18, 31, 10,

                    2, 8, 24, 14,

                    32, 27, 3, 9,

                    19, 13, 30, 6,

                    22, 11, 4, 25 };

    cout << endl;

    for (int i = 0; i < 16; i++) {

        // Expansion D-box

        string right_expanded = permute(right, exp_d, 48);

        // XOR RoundKey[i] and right_expanded

        string x = xor_(rkb[i], right_expanded);

        // S-boxes

        string op = "";

        for (int i = 0; i < 8; i++) {

            int row = 2 * int(x[i * 6] - '0') + int(x[i * 6 + 5] - '0');

            int col = 8 * int(x[i * 6 + 1] - '0') + 4 * int(x[i * 6 + 2] - '0') + 2 * int(x[i * 6 + 3] - '0') + int(x[i * 6 + 4] - '0');

            int val = s[i][row][col];

            op += char(val / 8 + '0');

            val = val % 8;

            op += char(val / 4 + '0');

            val = val % 4;

            op += char(val / 2 + '0');

            val = val % 2;

            op += char(val + '0');

        }

        // Straight D-box

        op = permute(op, per, 32);

        // XOR left and op

        x = xor_(op, left);

        left = x;

        // Swapper

        if (i != 15) {

            swap(left, right);

        }

        cout << "Round " << i + 1 << " " << bin2hex(left) << " "

             << bin2hex(right) << " " << rk[i] << endl;

    }

    // Combination

    string combine = left + right;

    // Final Permutation Table

    int final_perm[64] = { 40, 8, 48, 16, 56, 24, 64, 32,

                           39, 7, 47, 15, 55, 23, 63, 31,

                           38, 6, 46, 14, 54, 22, 62, 30,

                           37, 5, 45, 13, 53, 21, 61, 29,

                           36, 4, 44, 12, 52, 20, 60, 28,

                           35, 3, 43, 11, 51, 19, 59, 27,

                           34, 2, 42, 10, 50, 18, 58, 26,

                           33, 1, 41, 9, 49, 17, 57, 25 };

    // Final Permutation

    string cipher = bin2hex(permute(combine, final_perm, 64));

    return cipher;

}

int main()

{

    // pt is plain text

    string pt, key;

    /*cout<<"Enter plain text(in hexadecimal): ";

    cin>>pt;

    cout<<"Enter key(in hexadecimal): ";

    cin>>key;*/

    pt = "123456ABCD132536";

    key = "AABB09182736CCDD";

    // Key Generation

    // Hex to binary

    key = hex2bin(key);

    // Parity bit drop table

    int keyp[56] = { 57, 49, 41, 33, 25, 17, 9,

                     1, 58, 50, 42, 34, 26, 18,

                     10, 2, 59, 51, 43, 35, 27,

                     19, 11, 3, 60, 52, 44, 36,

                     63, 55, 47, 39, 31, 23, 15,

                     7, 62, 54, 46, 38, 30, 22,

                     14, 6, 61, 53, 45, 37, 29,

                     21, 13, 5, 28, 20, 12, 4 };

    // getting 56 bit key from 64 bit using the parity bits

    key = permute(key, keyp, 56); // key without parity

    // Number of bit shifts

    int shift_table[16] = { 1, 1, 2, 2,

                            2, 2, 2, 2,

                            1, 2, 2, 2,

                            2, 2, 2, 1 };

    // Key- Compression Table

    int key_comp[48] = { 14, 17, 11, 24, 1, 5,

                         3, 28, 15, 6, 21, 10,

                         23, 19, 12, 4, 26, 8,

                         16, 7, 27, 20, 13, 2,

                         41, 52, 31, 37, 47, 55,

                         30, 40, 51, 45, 33, 48,

                         44, 49, 39, 56, 34, 53,

                         46, 42, 50, 36, 29, 32 };

    // Splitting

    string left = key.substr(0, 28);

    string right = key.substr(28, 28);

    vector<string> rkb; // rkb for RoundKeys in binary

    vector<string> rk; // rk for RoundKeys in hexadecimal

    for (int i = 0; i < 16; i++) {

        // Shifting

        left = shift_left(left, shift_table[i]);

        right = shift_left(right, shift_table[i]);

        // Combining

        string combine = left + right;

        // Key Compression

        string RoundKey = permute(combine, key_comp, 48);

        rkb.push_back(RoundKey);

        rk.push_back(bin2hex(RoundKey));

    }

    cout << "\nEncryption:\n\n";

    string cipher = encrypt(pt, rkb, rk);

    cout << "\nCipher Text: " << cipher << endl;

    cout << "\nDecryption\n\n";

    reverse(rkb.begin(), rkb.end());

    reverse(rk.begin(), rk.end());

    string text = encrypt(cipher, rkb, rk);

    cout << "\nPlain Text: " << text << endl;

}

Output: 

Encryption:After initial permutation: 14A7D67818CA18ADAfter splitting: L0=14A7D678 R0=18CA18ADRound 1 18CA18AD 5A78E394 194CD072DE8CRound 2 5A78E394 4A1210F6 4568581ABCCERound 3 4A1210F6 B8089591 06EDA4ACF5B5Round 4 B8089591 236779C2 DA2D032B6EE3Round 5 236779C2 A15A4B87 69A629FEC913Round 6 A15A4B87 2E8F9C65 C1948E87475ERound 7 2E8F9C65 A9FC20A3 708AD2DDB3C0Round 8 A9FC20A3 308BEE97 34F822F0C66DRound 9 308BEE97 10AF9D37 84BB4473DCCCRound 10 10AF9D37 6CA6CB20 02765708B5BFRound 11 6CA6CB20 FF3C485F 6D5560AF7CA5Round 12 FF3C485F 22A5963B C2C1E96A4BF3Round 13 22A5963B 387CCDAA 99C31397C91FRound 14 387CCDAA BD2DD2AB 251B8BC717D0Round 15 BD2DD2AB CF26B472 3330C5D9A36DRound 16 19BA9212 CF26B472 181C5D75C66DCipher Text: C0B7A8D05F3A829CDecryptionAfter initial permutation: 19BA9212CF26B472After splitting: L0=19BA9212 R0=CF26B472Round 1 CF26B472 BD2DD2AB 181C5D75C66DRound 2 BD2DD2AB 387CCDAA 3330C5D9A36DRound 3 387CCDAA 22A5963B 251B8BC717D0Round 4 22A5963B FF3C485F 99C31397C91FRound 5 FF3C485F 6CA6CB20 C2C1E96A4BF3Round 6 6CA6CB20 10AF9D37 6D5560AF7CA5Round 7 10AF9D37 308BEE97 02765708B5BFRound 8 308BEE97 A9FC20A3 84BB4473DCCCRound 9 A9FC20A3 2E8F9C65 34F822F0C66DRound 10 2E8F9C65 A15A4B87 708AD2DDB3C0Round 11 A15A4B87 236779C2 C1948E87475ERound 12 236779C2 B8089591 69A629FEC913Round 13 B8089591 4A1210F6 DA2D032B6EE3Round 14 4A1210F6 5A78E394 06EDA4ACF5B5Round 15 5A78E394 18CA18AD 4568581ABCCERound 16 14A7D678 18CA18AD 194CD072DE8CPlain Text: 123456ABCD132536